The definition of convergence says that for any ε (so someone could pick it as small as they want to) there exists an N (integer: 1,2,3,..) such that for n>N |S-Sn|<ε. So if they said ε = 1, |S-S1|=|1 -1/2|=1/2<1=ε. So N=1, and for any n>1, |S-Sn|<ε is still true.